few_shots: Example:
Problem/activity:
Problem 1
The table below contains single equations in a single variable, single equations in two variables, and pairs of simultaneous equations in two variables. Check the appropriate box to show whether there is no solution, exactly 1 solution, or if there is an infinite number of solutions.
|                                                          | **           No solution          ** | **           Exactly 1 solution          ** | **           Infinite number of solutions          ** |
|----------------------------------------------------------|--------------------------------------|---------------------------------------------|-------------------------------------------------------|
|                       $${9=4x+7}$$                       |                                      |                                             |                                                       |
|                       $${y=3y+5}$$                       |                                      |                                             |                                                       |
|                    $${y={x\over2}}$$                     |                                      |                                             |                                                       |
|                     $${3x+6y-9=0}$$                      |                                      |                                             |                                                       |
|    $${x=y}$$                        $${1.25x=1.25y}$$    |                                      |                                             |                                                       |
| $${9.9=6x+8y}$$                        $${9x=2.5y-8.8}$$ |                                      |                                             |                                                       |
| $${11x-2y=1.5}$$                        $${11x-2y=2.5}$$ |                                      |                                             |                                                       |
Problem 2
Kim has a small container and a large container as shown.
[IMG]
It takes 16 of the small containers to fill the large container. Three small containers leave 1.95 gallons of space in the big container.
What is the size of each of the two containers?


Standard options: 
A. Solve linear equations in one variable.
B. Analyze and solve pairs of simultaneous linear equations.


Thought: The last three rows of the table in the first problem involves solving pairs of simultaneous linear equations. The second word problem can also be represented as two simultaneous linear equations.
Answer: B

Now, assign the following problem or activity to one or more relevant standards it aligns with.
shot_info: fl_problem_001392

8
options: Fluently add and subtract within 5.

Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).

Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.

Represent addition and subtraction with objects, fingers, mental images, drawings (Drawings need not show details, but should show the mathematics in the problem. (This applies wherever drawings are mentioned in the Standards.)), sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.

For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation.
problem_activity: Narrative
The purpose of this activity is for students to make connections between written numbers and expressions. In the activity synthesis, students see each teen number written as an equation. In this unit, when reading equations to students, read the equal sign as “is.” For example, read
\(10 + 3 = 13\)
as “10 plus 3 is 13.” The equal sign will be read as “equals” in the next unit.
MLR8 Discussion Supports.
Synthesis: At the appropriate time, give students 2–3 minutes to make sure that everyone in their group can explain how they organized the numbers and expressions. Invite groups to rehearse what they will say when they share with the whole class.
Advances: Speaking, Conversing, Representing
Engagement: Develop Effort and Persistence.
Some students would benefit from having clear examples of the expectation of group work in this activity. Invite students to generate a list of shared expectations for group work. Ask students to share explicit examples of what those expectations would look like in this activity.
Supports accessibility for: Social-Emotional Functioning
Required Materials
Materials to Copy
Numbers and Expressions Cards
Required Preparation
Create a set of cards from the blackline master for each group of 4.
Launch
Groups of 4
Give each group of students a set of cards.
“Work with your group to organize the cards in a way that makes sense to you.”
Activity
6 minutes: small-group work time
Monitor for students who organize the numbers and expressions as shown in the sample response.
Student Response
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Activity Synthesis
Invite a group of students to share how they organized the numbers and expressions or display the image in student responses.
“What do you notice about the numbers and expressions when they are arranged this way?” (They’re in the order that we count. The first number stays the same. The second number is 1 more each time. All the expressions have a 10. The second number starts at 1 and is one more each time. The expressions match the numbers.)
“Which number does
\(10 + 1\)
represent? How do you know?” (11)
“
\(10 + 1\)
is 11. We can write that as
\(10 + 1 = 11\)
.”
Demonstrate writing equations for each number and expression.


correct_option_index: 3